Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot StdAge}{k+StdAge}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(StdAge\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FI A data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot StdAge} {k+StdAge} \right)\)

sub-model b: s form \(\left( \frac {A \cdot StdAge^s} {k^s+StdAge^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot StdAge^s} {k^s + StdAge^s} \right)\)

Note:

This analysis uses ALL available plot biomass data

which includes the following plot-based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9938     2556.7                                
## 2   9937     2541.4  1 15.341  59.985 1.049e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107909.7
## 2     2 107851.8
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.383270   0.101114  -3.790 0.000151 ***
## phi   0.052775   0.006569   8.034 1.05e-15 ***
## A   556.613146  34.179453  16.285  < 2e-16 ***
## k   245.186030  17.581092  13.946  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5057 on 9937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.762e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   9937     2541.4                          
## 2   9936     2540.9  1 0.48648  1.9024 0.1678
##   model      AIC
## 1     2 107851.8
## 2    2a 107851.9
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.383270   0.101114  -3.790 0.000151 ***
## phi   0.052775   0.006569   8.034 1.05e-15 ***
## A   556.613146  34.179453  16.285  < 2e-16 ***
## k   245.186030  17.581092  13.946  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5057 on 9937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.762e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1  30370      10683                         
## 2  30361      10682  9  1.207  0.3812 0.9447
##   model      AIC
## 1     1 316873.0
## 2     2 316790.5
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.003487   0.062219   0.056    0.955    
## phi  -0.005058   0.003123  -1.620    0.105    
## A   208.607545   4.439034  46.994   <2e-16 ***
## k    91.158802   2.492202  36.578   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5932 on 30361 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.498e-06
##   (30 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1  30361      10682                              
## 2  30360      10662  1  19.84  56.491 5.8e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 316790.5
## 2    2a 316736.1
## 3    2b 316780.2
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.023795   0.061696  -0.386     0.70    
## phi  -0.004728   0.003120  -1.516     0.13    
## A   230.695658   7.026466  32.832  < 2e-16 ***
## k   112.039694   5.271333  21.255  < 2e-16 ***
## p     0.013745   0.001721   7.985 1.45e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5926 on 30360 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.723e-06
##   (30 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1  11289     2126.3                           
## 2  11288     2126.3  1 0.027622  0.1466 0.7018
##   model      AIC
## 1     1 123755.5
## 2     2 123757.4
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.03093    0.07355  -0.421    0.674    
## A  494.44302   21.74831  22.735   <2e-16 ***
## k  158.15402    8.54362  18.511   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.434 on 11289 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.7e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  11289     2126.3                          
## 2  11288     2126.2  1 0.10645  0.5652 0.4522
##   model      AIC
## 1     1 123755.5
## 2    1a 123756.9
## 3    1b       NA
## 4    1c       NA
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.03093    0.07355  -0.421    0.674    
## A  494.44302   21.74831  22.735   <2e-16 ***
## k  158.15402    8.54362  18.511   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.434 on 11289 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.7e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7909     2647.4                          
## 2   7908     2647.2  1 0.21999  0.6572 0.4176
##   model      AIC
## 1     1 85472.19
## 2     2 85473.53
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.2451     0.1104   -2.22   0.0264 *  
## A  528.2512    42.9834   12.29   <2e-16 ***
## k  242.8753    22.7556   10.67   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5786 on 7909 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.799e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   7909     2647.4                              
## 2   7908     2644.2  1 3.1482  9.4151 0.002159 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85472.19
## 2    1a 85464.77
## 3    1b       NA
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  -0.229136   0.111317  -2.058   0.0396 *  
## A  449.068734  41.427170  10.840  < 2e-16 ***
## k  189.508155  23.529869   8.054 9.19e-16 ***
## p   -0.008452   0.003651  -2.315   0.0206 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5783 on 7908 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.275e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13436     2603.2                                
## 2  13435     2600.1  1 3.1828  16.446 5.034e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 140769.3
## 2     2 140754.9
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.059184   0.072709   0.814    0.416    
## phi  -0.018594   0.004521  -4.113 3.93e-05 ***
## A   238.276645   6.455550  36.910  < 2e-16 ***
## k    73.287908   2.872621  25.513  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4399 on 13435 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.823e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1  13435     2600.1                               
## 2  13434     2600.1  1  0.0004   0.0021 0.9635    
## 3  13434     2593.9  0  0.0000                    
## 4  13433     2571.9  1 21.9779 114.7902 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 140754.9
## 2    2a 140756.9
## 3    2b 140724.9
## 4    2c 140612.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.082410   0.073052   1.128 0.259296    
## phi  -0.016545   0.004501  -3.675 0.000238 ***
## A   144.478610   3.756822  38.458  < 2e-16 ***
## k    38.479465   1.013132  37.981  < 2e-16 ***
## p     0.145366   0.012293  11.825  < 2e-16 ***
## s     2.115570   0.105329  20.085  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4376 on 13433 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.699e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1  19932     6444.3                            
## 2  19931     6442.9  1 1.4098  4.3612 0.03678 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 217634.0
## 2     2 217631.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.635113   0.075632   8.397   <2e-16 ***
## phi  -0.008778   0.004210  -2.085   0.0371 *  
## A   273.716406   6.200726  44.143   <2e-16 ***
## k    66.637249   1.817470  36.665   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5686 on 19931 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.649e-06
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  19931     6442.9                                 
## 2  19930     6390.5  1  52.413  163.46 < 2.2e-16 ***
## 3  19930     6434.4  0   0.000                      
## 4  19929     6321.2  1 113.247  357.04 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 217631.6
## 2    2a 217470.8
## 3    2b 217607.5
## 4    2c 217255.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.696041   0.076247   9.129   <2e-16 ***
## phi  -0.009557   0.004162  -2.296   0.0217 *  
## A   174.697261   4.714684  37.054   <2e-16 ***
## k    33.390061   1.183674  28.209   <2e-16 ***
## p     0.070684   0.003851  18.354   <2e-16 ***
## s     1.626479   0.045572  35.690   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5632 on 19929 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.992e-06
##   (26 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  20858     9688.4                                
## 2  20855     9677.1  3 11.326  8.1366 2.065e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 232500.8
## 2     2 232460.1
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.23827    0.07490   3.181  0.00147 ** 
## phi   0.01426    0.00516   2.763  0.00574 ** 
## A   300.75555    8.24620  36.472  < 2e-16 ***
## k    76.56971    2.56518  29.850  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6812 on 20855 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.192e-07
##   (60 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  20855     9677.1                                 
## 2  20854     9613.9  1  63.196  137.08 < 2.2e-16 ***
## 3  20854     9664.0  0   0.000                      
## 4  20853     9549.8  1 114.204  249.38 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 232460.1
## 2    2a 232325.5
## 3    2b 232434.0
## 4    2c 232188.0
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  2.429e-01  7.416e-02   3.275  0.00106 ** 
## phi 1.507e-02  5.119e-03   2.944  0.00324 ** 
## A   1.943e+02  6.621e+00  29.353  < 2e-16 ***
## k   3.837e+01  1.793e+00  21.402  < 2e-16 ***
## p   6.184e-02  4.309e-03  14.349  < 2e-16 ***
## s   1.554e+00  5.041e-02  30.828  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6767 on 20853 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.006e-06
##   (60 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   2186     817.40                            
## 2   2185     815.82  1 1.5791  4.2294 0.03985 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24934.44
## 2     2 24932.20
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.12226    0.23290  -0.525   0.5997    
## phi   0.03788    0.01859   2.037   0.0417 *  
## A   531.80592   74.36941   7.151 1.17e-12 ***
## k   161.97411   27.41420   5.908 4.00e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.611 on 2185 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.058e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   2185     815.82                              
## 2   2184     814.69  1 1.1257  3.0176 0.082505 . 
## 3   2184     815.53  0 0.0000                    
## 4   2183     813.00  1 2.5343  6.8049 0.009153 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 24932.20
## 2    2a 24931.18
## 3    2b 24933.42
## 4    2c 24928.61
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.13384    0.23173  -0.578   0.5636    
## phi   0.03911    0.01856   2.107   0.0352 *  
## A   315.56482   79.16136   3.986 6.93e-05 ***
## k    72.27038   23.67493   3.053   0.0023 ** 
## p     0.04870    0.02473   1.969   0.0490 *  
## s     1.45175    0.24454   5.937 3.38e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6103 on 2183 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.444e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89517, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.499, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    242     62.060                          
## 2    241     61.802  1 0.25746   1.004 0.3174
##   model      AIC
## 1     1 3072.961
## 2     2 3073.942
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   -0.5707     0.4891  -1.167 0.244465    
## A  1512.2130   452.0474   3.345 0.000953 ***
## k   283.3775    89.0654   3.182 0.001656 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5064 on 242 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.901e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    242     62.060                             
## 2    241     61.245  1 0.81471  3.2059 0.07463 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3072.961
## 2    1a 3071.723
## 3    1b       NA
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.58798    0.48266  -1.218 0.224336    
## A  1176.06873  341.99673   3.439 0.000688 ***
## k   176.81762   69.54297   2.543 0.011631 *  
## p    -0.02765    0.02296  -1.204 0.229626    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5041 on 241 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.632e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96346, p-value = 6.668e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.2838, p-value = 0.001024
## alternative hypothesis: two.sided

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   2781     760.98                           
## 2   2780     760.95  1 0.034127  0.1247  0.724
##   model      AIC
## 1     1 29399.95
## 2     2 29401.83
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3455     0.1580  -2.187   0.0289 *  
## A  303.2515    24.8271  12.215   <2e-16 ***
## k  114.1674    11.9374   9.564   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5231 on 2781 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.755e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   2781     760.98                             
## 2   2780     760.17  1 0.81064  2.9646 0.08522 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29399.95
## 2    1a 29398.99
## 3    1b 29390.81
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + 
##     STDAGE^s))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3165     0.1596  -1.983   0.0475 *  
## A  191.1468    18.4763  10.345  < 2e-16 ***
## k   50.8835     7.0584   7.209 7.23e-13 ***
## s    1.3703     0.1031  13.288  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5222 on 2780 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.049e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96263, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -24.432, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1282     497.71                           
## 2   1281     497.68  1 0.026566  0.0684 0.7938
##   model      AIC
## 1     1 13108.71
## 2     2 13110.64
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.4374     0.2635  -1.660   0.0971 .  
## A  220.2286    25.1890   8.743  < 2e-16 ***
## k   82.2162    11.9149   6.900 8.14e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6231 on 1282 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.21e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1282     497.71                           
## 2   1281     497.69  1 0.022344  0.0575 0.8105
##   model      AIC
## 1     1 13108.71
## 2    1a 13110.66
## 3    1b 13102.40
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + 
##     STDAGE^s))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.4803     0.2575  -1.865   0.0624 .  
## A  134.9472    16.4694   8.194 6.07e-16 ***
## k   33.0748     5.9587   5.551 3.46e-08 ***
## s    1.4034     0.1365  10.279  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6213 on 1281 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 9.017e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94897, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.208, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Error in nls(f_1, data = P_261, start = c(ge = ge.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Warning: Unknown or uninitialised column: `nls_weights.2`.
##   model      AIC
## 1     1       NA
## 2     2 736.1474
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)   
## ge    5.60183    6.70319   0.836  0.40715   
## phi   0.19470    0.09691   2.009  0.04974 * 
## A   566.24038  333.12863   1.700  0.09515 . 
## k   215.25516   71.78356   2.999  0.00415 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 164.3 on 52 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.205e-06

summary

  • simple model: does not fit
  • phi model: fits

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_262.' not found

summary

  • simple model: does not fit
  • phi model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    426     98.090                            
## 2    425     97.026  1 1.0635  4.6584 0.03146 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5410.292
## 2     2 5407.615
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.29301    0.68606   1.885   0.0602 .  
## phi   -0.08221    0.03786  -2.171   0.0305 *  
## A   1049.16808  209.39393   5.010 7.98e-07 ***
## k    224.28333   45.52407   4.927 1.20e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4778 on 425 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.113e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_263,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    425     97.026                          
## 2    424     96.827  1 0.19956  0.8739 0.3504
##   model      AIC
## 1     2 5407.615
## 2    2a 5408.732
## 3    2b 5404.762
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   1.558e+00  7.516e-01   2.073   0.0388 *  
## phi -6.898e-02  3.817e-02  -1.807   0.0715 .  
## A    5.777e+03  1.342e+04   0.430   0.6672    
## k    4.975e+03  1.915e+04   0.260   0.7952    
## s    7.450e-01  1.037e-01   7.185 3.04e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4757 on 424 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 2.064e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97891, p-value = 6.856e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8867, p-value = 3.94e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    503     197.73                            
## 2    502     196.55  1 1.1824  3.0198 0.08287 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5500.917
## 2     2 5499.883
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.74878    0.45224  -1.656 0.098404 .  
## phi  -0.06604    0.04231  -1.561 0.119148    
## A   198.37376   34.24510   5.793 1.22e-08 ***
## k   126.91926   32.37995   3.920 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6257 on 502 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.528e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    502     196.55                          
## 2    501     196.12  1 0.42914  1.0963 0.2956
##   model      AIC
## 1     2 5499.883
## 2    2a 5500.777
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.74878    0.45224  -1.656 0.098404 .  
## phi  -0.06604    0.04231  -1.561 0.119148    
## A   198.37376   34.24510   5.793 1.22e-08 ***
## k   126.91926   32.37995   3.920 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6257 on 502 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.528e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89169, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5305, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1     13     3559.6                         
## 2     12     3499.8  1 59.729  0.2048  0.659
##   model      AIC
## 1     1 139.8829
## 2     2 141.6121
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## ge   -1.737      1.176  -1.477    0.163
## A   119.386    102.105   1.169    0.263
## k   101.084    115.067   0.878    0.396
## 
## Residual standard error: 16.55 on 13 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.662e-06

summary

  • simple model: fits
  • phi model: fits

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

## Error in nls(f_1, data = P_321, start = c(ge = ge.start, A = A.start,  : 
##   singular gradient
## Error in nls(f_2, data = P_321, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_321$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_321.' not found

summary

  • simple model: does not fit
  • phi model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1      5     5487.1                         
## 2      4     5479.9  1 7.2366  0.0053 0.9456
##   model      AIC
## 1     1 82.94879
## 2     2 84.93823
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge    3.598     13.618   0.264   0.8022  
## A    20.616     37.917   0.544   0.6100  
## k   -78.208     32.792  -2.385   0.0628 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 33.13 on 5 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.894e-06

summary

  • simple model: fits
  • phi model: fits

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    749     502.27                         
## 2    748     500.96  1 1.3185  1.9687  0.161
##   model      AIC
## 1     1 7643.027
## 2     2 7643.050
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3773     0.5245  -0.719    0.472    
## A  111.0018    18.8722   5.882 6.12e-09 ***
## k   78.2492    16.6590   4.697 3.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8189 on 749 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.308e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    749     502.27                                
## 2    748     501.49  1  0.786  1.1724    0.2793    
## 3    748     502.02  0  0.000                      
## 4    747     489.77  1 12.249 18.6829 1.753e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7643.027
## 2    1a 7643.849
## 3    1b 7644.646
## 4    1c 7628.070
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge -0.15646    0.56610  -0.276 0.782335    
## A  58.03452    7.69556   7.541 1.35e-13 ***
## k  33.19091    3.02797  10.961  < 2e-16 ***
## p   0.18739    0.03023   6.199 9.39e-10 ***
## s   3.92007    1.13605   3.451 0.000591 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8097 on 747 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.363e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86401, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.021, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    319     225.08                          
## 2    318     224.66  1 0.41885  0.5929 0.4419
##   model      AIC
## 1     1 3495.454
## 2     2 3496.854
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.2726     0.8399  -0.325   0.7457  
## A  221.7114   101.3257   2.188   0.0294 *
## k  111.7604    64.6879   1.728   0.0850 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.84 on 319 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.338e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    319     225.08                         
## 2    317     222.68  2 2.4005  1.7086 0.1828
##   model      AIC
## 1     1 3495.454
## 2    1a       NA
## 3    1b       NA
## 4    1c 3496.001
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.2726     0.8399  -0.325   0.7457  
## A  221.7114   101.3257   2.188   0.0294 *
## k  111.7604    64.6879   1.728   0.0850 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.84 on 319 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.338e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84817, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.635, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    143     47.408                            
## 2    142     47.404  1 0.0038133  0.0114  0.915
##   model      AIC
## 1     1 1571.465
## 2     2 1573.453
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge    1.456      1.492   0.976  0.33092   
## A   167.149     63.483   2.633  0.00939 **
## k   137.477     57.992   2.371  0.01909 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5758 on 143 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.806e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    143     47.408                          
## 2    142     47.292  1 0.11632  0.3493 0.5555
##   model      AIC
## 1     1 1571.465
## 2    1a 1573.107
## 3    1b 1572.451
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge    1.456      1.492   0.976  0.33092   
## A   167.149     63.483   2.633  0.00939 **
## k   137.477     57.992   2.371  0.01909 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5758 on 143 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.806e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97471, p-value = 0.008393
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.7953, p-value = 0.0001475
## alternative hypothesis: two.sided

predict and plot

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    316     248.86                         
## 2    315     247.20  1 1.6645  2.1211 0.1463
##   model      AIC
## 1     1 3398.076
## 2     2 3397.935
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.40249    0.86776  -0.464 0.643092    
## phi -0.08326    0.06173  -1.349 0.178367    
## A   93.05864   24.23433   3.840 0.000149 ***
## k   57.11574   19.87840   2.873 0.004339 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8859 on 315 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.331e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    315     247.20                              
## 2    314     246.66  1 0.5323  0.6776 0.411031   
## 3    314     245.51  0 0.0000                    
## 4    313     237.31  1 8.1965 10.8108 0.001124 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3397.935
## 2    2a 3399.247
## 3    2b 3397.748
## 4    2c 3388.916
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.17078    0.93933  -0.182  0.85585    
## phi -0.09125    0.06151  -1.483  0.13895    
## A   61.58942   14.70342   4.189 3.65e-05 ***
## k   45.99393    8.86531   5.188 3.83e-07 ***
## p    0.26680    0.08890   3.001  0.00291 ** 
## s    3.40745    1.74208   1.956  0.05136 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8707 on 313 degrees of freedom
## 
## Number of iterations to convergence: 19 
## Achieved convergence tolerance: 9.465e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87835, p-value = 3.319e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.3789, p-value = 7.496e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

411 - Everglades

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    166     71.634                                
## 2    165     67.027  1 4.6065   11.34 0.0009441 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1787.685
## 2     2 1778.452
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    -1.7989     0.4433  -4.058 7.62e-05 ***
## phi   -0.3428     0.1230  -2.786  0.00596 ** 
## A   1605.1761  3041.3144   0.528  0.59835    
## k    764.0349  1516.4489   0.504  0.61505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6374 on 165 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.365e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_411,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_411,  : 
##   singular gradient
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_411,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     2 1778.452
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    -1.7989     0.4433  -4.058 7.62e-05 ***
## phi   -0.3428     0.1230  -2.786  0.00596 ** 
## A   1605.1761  3041.3144   0.528  0.59835    
## k    764.0349  1516.4489   0.504  0.61505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6374 on 165 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.365e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97702, p-value = 0.006624
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.826, p-value = 1.393e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10057     2001.3                                
## 2  10056     1994.5  1 6.8491  34.532 4.325e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107037.0
## 2     2 107004.5
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  8.733e-02  9.286e-02    0.94    0.347    
## phi 3.115e-02  5.504e-03    5.66 1.56e-08 ***
## A   4.790e+02  2.391e+01   20.03  < 2e-16 ***
## k   2.205e+02  1.280e+01   17.23  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4454 on 10056 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.401e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10056     1994.5                                
## 2  10055     1987.0  1 7.4779  37.841 7.967e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 107004.5
## 2    2a 106968.7
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.054423   0.091634   0.594    0.553    
## phi   0.030372   0.005481   5.541 3.08e-08 ***
## A   377.503856  20.268188  18.625  < 2e-16 ***
## k   144.875032  12.158229  11.916  < 2e-16 ***
## p    -0.021206   0.004829  -4.391 1.14e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4445 on 10055 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.957e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13160     2210.7                                
## 2  13159     2191.1  1 19.627  117.87 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 145414.7
## 2     2 145299.3
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.548961   0.071191   7.711 1.34e-14 ***
## phi  -0.038971   0.003549 -10.980  < 2e-16 ***
## A   271.111248   6.089184  44.523  < 2e-16 ***
## k    63.850565   2.100846  30.393  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4081 on 13159 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.803e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1  13159     2191.1                              
## 2  13158     2191.0  1  0.052   0.3099 0.5777    
## 3  13158     2178.8  0  0.000                    
## 4  13157     2146.2  1 32.590 199.7893 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 145299.3
## 2    2a 145301.0
## 3    2b 145227.4
## 4    2c 145031.0
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.642941   0.073275   8.774   <2e-16 ***
## phi  -0.037296   0.003508 -10.631   <2e-16 ***
## A   170.328853   3.502018  48.637   <2e-16 ***
## k    37.150549   0.741208  50.122   <2e-16 ***
## p     0.165317   0.009961  16.596   <2e-16 ***
## s     2.342576   0.099384  23.571   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4039 on 13157 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.84e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1243     169.25                                
## 2   1242     166.62  1 2.6234  19.555 1.063e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 12649.64
## 2     2 12632.18
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.52664    0.15034  -3.503 0.000476 ***
## phi   0.06689    0.01592   4.202 2.84e-05 ***
## A   271.29836   24.43298  11.104  < 2e-16 ***
## k    83.42650   11.61984   7.180 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3663 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.432e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1242     166.62                           
## 2   1241     166.59  1 0.035854  0.2671 0.6054
## 3   1241     166.55  0 0.000000               
## 4   1240     166.53  1 0.028854  0.2149 0.6431
##   model      AIC
## 1     2 12632.18
## 2    2a 12633.91
## 3    2b 12633.65
## 4    2c 12635.43
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.52664    0.15034  -3.503 0.000476 ***
## phi   0.06689    0.01592   4.202 2.84e-05 ***
## A   271.29836   24.43298  11.104  < 2e-16 ***
## k    83.42650   11.61984   7.180 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3663 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.432e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97257, p-value = 1.24e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.49, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   1484     342.22                             
## 2   1483     341.30  1 0.92221  4.0072 0.04549 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15286.15
## 2     2 15284.13
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.15481    0.24948   0.621   0.5350    
## phi   0.03631    0.01849   1.964   0.0497 *  
## A   316.03672   38.38330   8.234 3.94e-16 ***
## k   142.92057   21.27357   6.718 2.61e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1483 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.777e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1483     341.30                           
## 2   1482     341.24  1 0.055697  0.2419 0.6229
## 3   1482     341.20  0 0.000000               
## 4   1481     341.19  1 0.008313  0.0361 0.8494
##   model      AIC
## 1     2 15284.13
## 2    2a 15285.89
## 3    2b 15285.71
## 4    2c 15287.68
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.15481    0.24948   0.621   0.5350    
## phi   0.03631    0.01849   1.964   0.0497 *  
## A   316.03672   38.38330   8.234 3.94e-16 ***
## k   142.92057   21.27357   6.718 2.61e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1483 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.777e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96927, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.614, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7934     4843.9                          
## 2   7933     4843.0  1 0.86271  1.4131 0.2346
##   model      AIC
## 1     1 105723.9
## 2     2 105724.4
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.02465    0.16455    0.15    0.881    
## A  780.98344   41.40997   18.86   <2e-16 ***
## k  223.08680   12.70480   17.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7814 on 7934 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.343e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7934     4843.9                                 
## 2   7933     4825.5  1 18.4033 30.2546 3.907e-08 ***
## 3   7932     4825.3  1  0.1519  0.2497    0.6173    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 105723.9
## 2    1a 105695.6
## 3    1b       NA
## 4    1c 105697.4
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   0.008305   0.163098   0.051    0.959    
## A  682.531690  36.459330  18.720  < 2e-16 ***
## k  159.113169  12.652352  12.576  < 2e-16 ***
## p   -0.033932   0.007527  -4.508 6.63e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7799 on 7933 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.717e-07
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

plot residuals

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4571     2296.8                                
## 2   4570     2264.8  1 32.069  64.711 1.096e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 57841.68
## 2     2 57779.37
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    2.35377    0.46352   5.078 3.96e-07 ***
## phi   0.10652    0.01124   9.476  < 2e-16 ***
## A   355.35507   27.88660  12.743  < 2e-16 ***
## k   148.96824   12.01719  12.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.704 on 4570 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.649e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   4570     2264.8                          
## 2   4569     2264.4  1 0.33289  0.6717 0.4125
## 3   4569     2264.7  0 0.00000               
## 4   4568     2264.2  1 0.49094  0.9905 0.3197
##   model      AIC
## 1     2 57779.37
## 2    2a 57780.69
## 3    2b 57781.25
## 4    2c 57782.26
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    2.35377    0.46352   5.078 3.96e-07 ***
## phi   0.10652    0.01124   9.476  < 2e-16 ***
## A   355.35507   27.88660  12.743  < 2e-16 ***
## k   148.96824   12.01719  12.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.704 on 4570 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.649e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91632, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -25.825, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Error in nls(f_1, data = P_M262, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Warning: Unknown or uninitialised column: `nls_weights.2`.
##   model      AIC
## 1     1       NA
## 2     2 615.3221
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   -1.8417     0.8477  -2.172  0.03459 *  
## phi  -0.3664     0.2019  -1.814  0.07561 .  
## A    84.9819    25.1232   3.383  0.00140 ** 
## k   -22.9322     5.4606  -4.200  0.00011 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 68.33 on 50 degrees of freedom
## 
## Number of iterations to convergence: 23 
## Achieved convergence tolerance: 6.694e-06

summary

  • simple model: does not fit
  • phi model: fits

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    909     284.47                          
## 2    908     284.00  1 0.46904  1.4996  0.221
##   model      AIC
## 1     1 9555.938
## 2     2 9556.433
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.9439     0.2374  -3.977 7.54e-05 ***
## A  393.0871    93.6950   4.195 2.99e-05 ***
## k  282.2375    85.6482   3.295  0.00102 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5594 on 909 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.158e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    909     284.47                          
## 2    908     284.31  1 0.16139  0.5154  0.473
##   model      AIC
## 1     1 9555.938
## 2    1a 9557.420
## 3    1b       NA
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.9439     0.2374  -3.977 7.54e-05 ***
## A  393.0871    93.6950   4.195 2.99e-05 ***
## k  282.2375    85.6482   3.295  0.00102 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5594 on 909 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.158e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9539, p-value = 2.596e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.6403, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   5206     1821.1                          
## 2   5205     1820.9  1 0.24737  0.7071 0.4004
##   model      AIC
## 1     1 54709.07
## 2     2 54710.37
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.97977    0.09812  -9.986   <2e-16 ***
## A  283.57736   14.79752  19.164   <2e-16 ***
## k  163.79765   11.57994  14.145   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5915 on 5206 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.7e-07
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)    
## 1   5206     1821.1                                
## 2   5205     1817.8  1  3.3414  9.5675 0.001991 ** 
## 3   5205     1820.9  0  0.0000                     
## 4   5204     1802.1  1 18.7736 54.2133 2.08e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 54709.07
## 2    1a 54701.51
## 3    1b 54710.31
## 4    1c 54658.33
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -1.00006    0.09689 -10.322   <2e-16 ***
## A  171.04159    8.60367  19.880   <2e-16 ***
## k   82.71515    4.09588  20.195   <2e-16 ***
## p    0.13600    0.01413   9.626   <2e-16 ***
## s    2.13334    0.17553  12.154   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5885 on 5204 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.463e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6772     3204.3                                
## 2   6771     3190.9  1 13.434  28.508 9.634e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 73901.46
## 2     2 73875.00
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.504e-01  1.856e-01   1.888   0.0591 .  
## phi 5.170e-02  9.073e-03   5.698 1.26e-08 ***
## A   2.253e+02  1.175e+01  19.184  < 2e-16 ***
## k   1.453e+02  8.485e+00  17.129  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6865 on 6771 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.071e-06
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   6771     3190.9                            
## 2   6770     3188.6  1 2.2882  4.8583 0.02755 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 73875.00
## 2    2a 73872.14
## 3    2b 73873.04
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.328e-01  1.846e-01   1.803   0.0715 .  
## phi 5.299e-02  9.054e-03   5.852 5.08e-09 ***
## A   2.401e+02  1.620e+01  14.816  < 2e-16 ***
## k   1.656e+02  1.637e+01  10.115  < 2e-16 ***
## p   8.549e-03  3.898e-03   2.193   0.0283 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6863 on 6770 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.081e-06
##   (5 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4434     1963.5                                
## 2   4433     1953.8  1 9.7019  22.012 2.791e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 49716.85
## 2     2 49696.87
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.31327    0.23183   1.351    0.177    
## phi   0.05343    0.01098   4.867 1.17e-06 ***
## A   353.28995   25.05730  14.099  < 2e-16 ***
## k   185.81962   13.58745  13.676  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6639 on 4433 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.849e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1   4433     1953.8                            
## 2   4432     1953.8  1 0.0054658  0.0124 0.9113
##   model      AIC
## 1     2 49696.87
## 2    2a 49698.86
## 3    2b 49654.37
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.31425    0.23062   1.363    0.173    
## phi   0.04752    0.01103   4.309 1.67e-05 ***
## A   227.37954   17.22538  13.200  < 2e-16 ***
## k    82.08926    8.13709  10.088  < 2e-16 ***
## s     1.29097    0.04711  27.405  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6606 on 4432 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.711e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93128, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -19.5, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    712     278.71                         
## 2    711     277.68  1 1.0259  2.6267 0.1055
##   model      AIC
## 1     1 7183.953
## 2     2 7183.316
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.26900    0.39205  -0.686    0.493    
## phi   0.03120    0.01943   1.606    0.109    
## A   119.13429   17.23489   6.912 1.06e-11 ***
## k    74.13118   16.35263   4.533 6.81e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6249 on 711 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.953e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_M334,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    711     277.68                          
## 2    710     277.10  1 0.57808  1.4812  0.224
##   model      AIC
## 1     2 7183.316
## 2    2a 7183.826
## 3    2b 7183.207
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge  -3.571e-01  3.791e-01  -0.942  0.34650   
## phi  3.184e-02  1.944e-02   1.638  0.10194   
## A    6.329e+02  2.290e+03   0.276  0.78232   
## k    3.062e+03  2.373e+04   0.129  0.89734   
## s    6.114e-01  2.046e-01   2.988  0.00291 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6245 on 710 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 4.116e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95815, p-value = 2.115e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5121, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    488     183.51                            
## 2    487     183.50  1 0.0097364  0.0258 0.8724
##   model      AIC
## 1     1 4999.077
## 2     2 5001.051
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.4407     0.2497  -5.769 1.42e-08 ***
## A  281.4947    47.5575   5.919 6.11e-09 ***
## k  196.9458    45.4153   4.337 1.76e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6132 on 488 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.962e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    488     183.51                           
## 2    487     183.48  1 0.030432  0.0808 0.7764
##   model      AIC
## 1     1 4999.077
## 2    1a 5000.996
## 3    1b 5000.193
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.4407     0.2497  -5.769 1.42e-08 ***
## A  281.4947    47.5575   5.919 6.11e-09 ***
## k  196.9458    45.4153   4.337 1.76e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6132 on 488 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.962e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92528, p-value = 6.539e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.105, p-value = 1.028e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2a
221 Eastern Broadleaf Forest 1
222 Midwest Broadleaf Forest 1a
223 Central Interior Broadleaf Forest 2c
231 Southeastern Mixed Forest 2c
232 Outer Coastal Plain Mixed Forest 2c
234 Lower Mississippi Riverine Forest 2c
242 Pacific Lowland Mixed Forest 1a
251 Prairie Parkland (Temperate) 1b
255 Prairie Parkland (Subtropical) 1b
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 2b
313 Colorado Plateau Semi-Desert 2
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 1c
332 Great Plains Steppe 1
341 Intermountain Semi-Desert and Desert 1
342 Intermountain Semi-Desert 2c
411 Everglades 2
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2a
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 1a
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 1
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 1c
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2b
M334 Black Hills Coniferous Forest 2b
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 1

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 9943 3257 -0.3832704 -0.5814740 -0.1850667 0.0527751 0.0398982 0.0656519 556.61315 489.61449 623.61180 245.18603 210.72352 279.64853
212 Laurentian Mixed Forest east 30395 11945 -0.0237945 -0.1447212 0.0971322 -0.0047284 -0.0108434 0.0013866 230.69566 216.92349 244.46783 112.03969 101.70766 122.37173
221 Eastern Broadleaf Forest east 11294 4269 -0.0309342 -0.1750956 0.1132271 NA NA NA 494.44302 451.81253 537.07350 158.15402 141.40703 174.90101
222 Midwest Broadleaf Forest east 7913 3189 -0.2291358 -0.4473468 -0.0109248 NA NA NA 449.06873 367.86054 530.27693 189.50815 143.38340 235.63291
223 Central Interior Broadleaf Forest east 13446 4895 0.0824103 -0.0607820 0.2256026 -0.0165446 -0.0253681 -0.0077211 144.47861 137.11471 151.84251 38.47946 36.49358 40.46535
231 Southeastern Mixed Forest east 19961 7904 0.6960411 0.5465897 0.8454924 -0.0095572 -0.0177145 -0.0013999 174.69726 165.45609 183.93843 33.39006 31.06996 35.71016
232 Outer Coastal Plain Mixed Forest east 20919 9046 0.2428901 0.0975352 0.3882451 0.0150706 0.0050373 0.0251038 194.33256 181.35574 207.30937 38.36687 34.85302 41.88072
234 Lower Mississippi Riverine Forest east 2190 937 -0.1338393 -0.5882767 0.3205981 0.0391064 0.0027170 0.0754959 315.56482 160.32533 470.80430 72.27038 25.84263 118.69814
242 Pacific Lowland Mixed Forest pacific 246 172 -0.5879779 -1.5387448 0.3627890 NA NA NA 1176.06873 502.38434 1849.75311 176.81762 39.82798 313.80727
251 Prairie Parkland (Temperate) east 2787 1036 -0.3164920 -0.6294917 -0.0034924 NA NA NA 191.14680 154.91806 227.37554 50.88350 37.04335 64.72365
255 Prairie Parkland (Subtropical) pacific 1288 659 -0.4803010 -0.9854995 0.0248975 NA NA NA 134.94717 102.63716 167.25718 33.07476 21.38485 44.76466
261 California Coastal Chaparral Forest and Shrub pacific 56 34 0.2076552 -2.1013650 2.5166754 NA NA NA 905.78231 218.48732 1593.07729 148.48112 17.92535 279.03690
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 430 274 1.5578428 0.0805959 3.0350898 -0.0689772 -0.1440026 0.0060482 5776.56204 -20609.55325 32162.67732 4974.62963 -32664.27955 42613.53881
313 Colorado Plateau Semi-Desert interior west 508 312 -0.7487763 -1.6372862 0.1397335 -0.0660397 -0.1491570 0.0170777 198.37376 131.09239 265.65513 126.91926 63.30235 190.53618
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 16 12 NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 22 14 NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 8 5 NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 753 473 -0.1564570 -1.2677922 0.9548782 NA NA NA 58.03452 42.92702 73.14201 33.19091 27.24656 39.13526
332 Great Plains Steppe interior west 324 152 -0.2725730 -1.9249635 1.3798175 NA NA NA 221.71144 22.36042 421.06247 111.76036 -15.50845 239.02916
341 Intermountain Semi-Desert and Desert interior west 147 93 1.4555092 -1.4936094 4.4046278 NA NA NA 167.14943 41.66251 292.63635 137.47725 22.84471 252.10980
342 Intermountain Semi-Desert interior west 320 222 -0.1707774 -2.0189835 1.6774286 -0.0912500 -0.2122765 0.0297764 61.58942 32.65939 90.51945 45.99393 28.55079 63.43707
411 Everglades east 170 86 -1.7989037 -2.6741478 -0.9236597 -0.3427743 -0.5857159 -0.0998326 1605.17611 -4399.73383 7610.08604 764.03493 -2230.11106 3758.18093
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 10063 3398 0.0544232 -0.1251974 0.2340437 0.0303723 0.0196282 0.0411165 377.50386 337.77416 417.23356 144.87503 121.04247 168.70759
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 13165 4970 0.6429412 0.4993110 0.7865714 -0.0372962 -0.0441726 -0.0304197 170.32885 163.46439 177.19331 37.15055 35.69767 38.60342
M223 Ozark Broadleaf Forest Meadow east 1248 392 -0.5266414 -0.8215878 -0.2316950 0.0668924 0.0356599 0.0981250 271.29836 223.36389 319.23283 83.42650 60.62982 106.22317
M231 Ouachita Mixed Forest east 1488 574 0.1548055 -0.3345582 0.6441691 0.0363124 0.0000483 0.0725765 316.03672 240.74538 391.32806 142.92057 101.19107 184.65006
M242 Cascade Mixed Forest pacific 7940 4900 0.0083049 -0.3114107 0.3280205 NA NA NA 682.53169 611.06181 754.00157 159.11317 134.31123 183.91511
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 4575 2761 2.3537716 1.4450510 3.2624922 0.1065227 0.0844846 0.1285608 355.35507 300.68386 410.02629 148.96824 125.40875 172.52773
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 54 38 NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 913 563 -0.9439044 -1.4097324 -0.4780764 NA NA NA 393.08713 209.20346 576.97081 282.23750 114.14629 450.32871
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 5236 3514 -1.0000591 -1.1899993 -0.8101190 NA NA NA 171.04159 154.17477 187.90840 82.71515 74.68551 90.74479
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 6780 4293 0.3327526 -0.0291287 0.6946338 0.0529865 0.0352378 0.0707352 240.08218 208.31663 271.84773 165.60474 133.50915 197.70032
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 4440 2838 0.3142512 -0.1378781 0.7663805 0.0475228 0.0259014 0.0691443 227.37954 193.60919 261.14989 82.08926 66.13650 98.04201
M334 Black Hills Coniferous Forest interior west 716 364 -0.3571166 -1.1014022 0.3871690 0.0318412 -0.0063321 0.0700145 632.93389 -3862.80228 5128.67006 3062.18270 -43518.70707 49643.07246
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 492 287 -1.4406677 -1.9313520 -0.9499835 NA NA NA 281.49475 188.05202 374.93748 196.94578 107.71211 286.17946

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot A (asymptote of B)

## Warning: Removed 7 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 7 rows containing missing values (geom_point).

Calculations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US   0.1591839
## 2       pacific   0.7449677
## 3          east   0.1495858
## 4 interior west  -0.1912246

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.008674616
## 2       pacific  0.031273796
## 3          east  0.001203679
## 4 interior west  0.025270797

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   310.7201
## 2       pacific   707.9920
## 3          east   268.4563
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   134.3730
## 2       pacific   296.7343
## 3          east    92.9108
## 4 interior west   201.8142

Calculations - weighted averages subsetted to 15 ecoprovinces

  • 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332,

ge

##          region weighted.ge
## 1     entire US   0.2665799
## 2       pacific   0.8536036
## 3          east   0.1757210
## 4 interior west   0.3327526

phi

##          region weighted.phi
## 1     entire US  0.009575266
## 2       pacific  0.038390439
## 3          east  0.001838774
## 4 interior west  0.052986482